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Two measures of effective population size for graphs
1Centre for Mathematical Science, City University, London, EC1V 0HB, United Kingdom. Mark.Broom.1@city.ac.uk
Evolution; International Journal of Organic Evolution
|April 24, 2012
Summary
This study introduces new formulas for effective population size in graph-based models, crucial for understanding genetic drift and evolution in structured populations. These methods aid in predicting genetic variation dynamics and mutation fixation probabilities.
Area of Science:
- Population Ecology
- Evolutionary Biology
- Theoretical Ecology
Background:
- Effective population size (Ne) is vital for predicting genetic variation, drift, and inbreeding.
- It influences fixation probabilities of advantageous and deleterious mutations.
- Graph-based models are increasingly used for structured populations, necessitating neutral evolution theory on graphs.
Purpose of the Study:
- Derive formulae for variance effective and inbreeding effective population sizes for general graphs.
- Relate these two measures of effective population size.
- Apply these formulae to specific graph structures like complete graphs, cycles, and bipartite graphs.
Main Methods:
- Derivation of analytical formulae for effective population size on unweighted, undirected graphs.
- Simulation-based estimation of inbreeding effective size for one-dimensional lattices and small-world graphs.
- Theoretical analysis of effective population size for complete, cycle, and bipartite graphs.
Main Results:
- Novel formulae for variance and inbreeding effective population sizes are presented for general graphs.
- The relationship between variance and inbreeding effective sizes is elucidated.
- Specific effective sizes are derived for complete, cycle, and bipartite graphs, with simulation estimates for lattices and small-world networks.
Conclusions:
- The derived formulae provide a theoretical framework for effective population size in structured populations modeled by graphs.
- This work extends neutral evolution theory to graph-based population structures.
- The methods are applicable to haploid populations with overlapping generations in various structured environments.
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